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Simplifying 9x2 + -30x + -5 = 0 Reorder the terms: -5 + -30x + 9x2 = 0 Solving -5 + -30x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -3.333333333x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -3.333333333x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -3.333333333x + x2 = 0 + 0.5555555556 -3.333333333x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -3.333333333x + x2 = 0.5555555556 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 0.5555555556 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 0.5555555556 + 2.777777779 Combine like terms: 0.5555555556 + 2.777777779 = 3.3333333346 2.777777779 + -3.333333333x + x2 = 3.3333333346 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 3.3333333346 Calculate the square root of the right side: 1.825741859 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.825741859 and -1.825741859.Subproblem 1
x + -1.666666667 = 1.825741859 Simplifying x + -1.666666667 = 1.825741859 Reorder the terms: -1.666666667 + x = 1.825741859 Solving -1.666666667 + x = 1.825741859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.825741859 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.825741859 + 1.666666667 x = 1.825741859 + 1.666666667 Combine like terms: 1.825741859 + 1.666666667 = 3.492408526 x = 3.492408526 Simplifying x = 3.492408526Subproblem 2
x + -1.666666667 = -1.825741859 Simplifying x + -1.666666667 = -1.825741859 Reorder the terms: -1.666666667 + x = -1.825741859 Solving -1.666666667 + x = -1.825741859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.825741859 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.825741859 + 1.666666667 x = -1.825741859 + 1.666666667 Combine like terms: -1.825741859 + 1.666666667 = -0.159075192 x = -0.159075192 Simplifying x = -0.159075192Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.492408526, -0.159075192}
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